Category THE ECONOMETRICS OF MACROECONOMIC MODELLING

In this section, we establish that money demand in the Euro area can be mod­elled with a simple equilibrium correction model. We base the empirical results on the work by Coenen and Vega (2001) who estimate the aggregate demand for broad money in the Euro area. In Table 8.1 we report a model which is a close approximation to their preferred specification for the quarterly growth

Table 8.1

Empirical model for Д(ш — p)t in the Euro area based onCoenen and Vega (2001)

We now relax the assumption of an exogenous interest rate in order to focus on monetary policy rules. We evaluate the performance of different types of reaction functions or interest rate rules using the small econo­metric model we developed, in Chapter 9. In addition to the standard efficiency measures, we look at the mean, deviations from targets, which may be of particular interest to policy makers. Specifically, we introduce the root mean squared target error (RMSTE), which is an analogue to the well known root mean squared forecast error. Throughout we assume that the monetary policy rules aim at stabilising inflation around an infla­tion target and that the monetary authorities also put some weight on stabilising unemployment, output, and interest rates...

The estimation of the P*-model in Section 8.5.4 requires additional data relative to the AWM data set. We have used a data series for broad money (M3) obtained from Gerlach and Svensson (2003) and Coenen and Vega (2001), which is shown in Figure 8.8.[74] It also requires transforms of the original data: Figures 8.9 and 8.10 show the price gap (p — p*)t and the real money gap

Figure 8.8. The M3 data series plotted against the shorter M3 series obtained from Gerlach and Svensson (2003), which in turn is based on data from Coenen and Vega (2001). Quarterly growth rate

Figure 8.9. The upper graphs show the GDP deflator and the equilibrium price level (p*), whereas the lower graph is their difference, that is, the price gap, used in the P*-model

In this section, we illustrate how the forecast errors of an EqCM and the corresponding dVAR are affected differently by structural breaks. Practical forecasting models are typically open systems, with exogenous variables. Although the model that we study in this section is of the simple kind, its properties will prove helpful in interpreting the forecasts errors of the large systems in Section 11.2.3.

A simple DGP This book has taken as a premise that macroeconomic time-series can be usefully viewed as integrated of order one, I(1), and that they also frequently include deterministic terms allowing for a linear trend. The following simple bivariate system (a first-order VAR) can serve as an example:

The main tools of evaluation of models like the NPCM have been the GMM test of validity of overidentifying restrictions (i. e. the xj-test earlier) and measures and graphs of goodness-of-fit.9 Neither of these tests is easy to interpret. First, the xj may have low power. Second, the estimation results reported by GG and GGL yield values of bp1 + bp1 close to 1 while the coefficient of the wage share is numerically small. This means that the apparently good fit is in fact no better (or worse) than a model in the double differences (e. g. a random walk); see Bardsen et al. (2002b). There is thus a need for other evaluation methods, and in the rest of this chapter we test the NPCM specification against alternative models of the inflation process.

When modelling the short-run relationships we impose the estimated steady state from (9.3) to (9.4) on a subsystem for {Awt, Apt} conditional on {Aat, Ayt, Aut-1, Apit, At1t, At3t} with all variables entering with two additional lags. In addition to energy prices Apet, we augment the system with {Aht, Wdumt, Pdumt} to capture short-run effects. Seasonalt is a centred seasonal dummy. The diagnostics of the unrestricted I(0) system are reported in the upper part of Table 9.2.

The short-run model is derived general to specific by deleting insignifi­cant terms, establishing a parsimonious statistical representation of the data in I(0)-space, following Hendry and Mizon (1993) and is found below: